Question

2cos(4x)+1/2cos(x)+1= (2cosx-1)*(2cos2x-1). Prove it.​

Answer 1

Answer:

$\frac{2\:cos4x+1}{2cosx+1}=(2cos2x-1)(2cosx-1)$

Step-by-step explanation:

$\frac{2\:cos4x+1}{2cosx+1}$

Using

$\boxed{cos2A=2\:cos^2A-1}$

$=\frac{2(2cos^22x-1)+1}{2cosx+1}$

$=\frac{4cos^22x-2+1}{2cosx+1}$

$=\frac{4cos^22x-1}{2cosx+1}$

$=\frac{(2cos2x)^2-1^2}{2cosx+1}$

Using

$\boxed{a^2-b^2=(a+b)(a-b)}$

$=\frac{(2cos2x-1)(2cos2x+1)}{2cosx+1}$

$=\frac{(2cos2x-1)(2(2cos^2x-1)+1)}{2cosx+1}$

$=\frac{(2cos2x-1)(4cos^2x-1)}{2cosx+1}$

$=\frac{(2cos2x-1)((2cosx)^2-1^2)}{2cosx+1}$

$=\frac{(2cos2x-1)(2cosx-1)(2cosx+1)}{2cosx+1}$

$=\frac{(2cos2x-1)(2cosx-1)}{1}$

$=(2cos2x-1)(2cosx-1)$

Answer 2

Answer:

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